STACKS & QUEUES

Presented by :- MANJU RANI

DATA STRUCTUR

E

LINEAR DATA STRUCTURE

ARRAY QUEUE STACK

NON LINEAR DATA

STRUCTURE

What is Linear Data Structure

In linear data structure, data is arranged in linear sequence.

 Data items can be traversed in a single run.

 In linear data structure elements are accessed or placed in contiguous(together in sequence) memory location. 

WHAT Is A stack is called a last-in-first-out (LIFO) collection. This means that the last thing we added (pushed) is the first thing that gets pulled (popped) off.

A stack is a sequence of items that are accessible at only one end of the sequence.

EXAMPLES OF STACK:

Operations that can be performed on STACK: PUSH.

POP.

PUSH : It is used to insert items into the stack.POP: It is used to delete items from stack.TOP: It represents the current location of data in stack.

ALGORITHM OF INSERTION IN STACK: (PUSH)1. Insertion(a,top,item,max)2. If top=max then print ‘STACK OVERFLOW’ exit else3. top=top+1 end if4. a[top]=item5. Exit

ALGORITHM OF DELETION IN STACK: (POP)

1. Deletion(a,top,item)2. If top=0 then print ‘STACK UNDERFLOW’ exit else3. item=a[top] end if4. top=top-15. Exit

ALGORITHM OF DISPLAY IN STACK:1.Display(top,i,a[i])2.If top=0 then Print ‘STACK EMPTY’ Exit Else3.For i=top to 0 Print a[i] End for4.exit

APPLICATIONS OF STACKS ARE:

I. Reversing Strings:• A simple application of stack is reversing

strings. To reverse a string , the characters of string are pushed onto the stack one by one as the string is read from left to right. • Once all the characters of string are pushed onto stack, they are popped one by one. Since the character last pushed in comes out first, subsequent pop operation results in the reversal of the string.

For example: To reverse the string ‘REVERSE’ the string is read from left to right and its characters are pushed . LIKE: onto a stack.

II. Checking the validity of an expression containing nested parenthesis:

• Stacks are also used to check whether a given

arithmetic expressions containing nested parenthesis is properly parenthesized.• The program for checking the validity of an expression verifies that for each left parenthesis braces or bracket ,there is a corresponding closing symbol and symbols are appropriately nested.

For example:VALID INPUTS INVALID INPUTS

{ }( { [ ] } ){ [ ] ( ) }[ { ( { } [ ] ( { })}]

{ ( }( [ ( ( ) ] ){ } [ ] )[ { ) } ( ] } ]

III. Evaluating arithmetic expressions:

INFIX notation: The general way of writing arithmetic expressions is known as infix notation. e.g, (a+b)

PREFIX notation: e.g, +AB

POSTFIX notation: e.g: AB+

Conversion of INFIX to POSTFIX conversion:Example: 2+(4-1)*3 step1 2+41-*3 step2 2+41-3* step3 241-3*+ step4

CURRENT SYMBOL

ACTION PERFORMED

STACK STATUS POSTFIX EXPRESSION

( PUSH C C 22 2+ PUSH + (+ 2( PUSH ( (+( 244 24- PUSH - (+(- 2411 POP 241-) (+ 241-* PUSH * (+* 241-3 241-3

POP * 241-3*POP + 241-3*+

)

CONVERSION OF INFIX INTO POSTFIX 2+(4-1)*3 into 241-3*+

Queues Queue is an ADT data structure similar to stack,

except that the first item to be inserted is the first one to be removed.

This mechanism is called First-In-First-Out (FIFO). Placing an item in a queue is called “insertion or

enqueue”, which is done at the end of the queue called “rear”.

Removing an item from a queue is called “deletion or dequeue”, which is done at the other end of the queue called “front”.

Some of the applications are : printer queue, keystroke queue, etc.

Operations On A Queue

1.To insert an element in queue

2.Delete an element from queue

The Queue OperationPlacing an item in a queue is called “insertion or enqueue”, which is done at the end of the queue called “rear”.

FrontRear

The Queue Operation Removing an item from a queue is called “deletion or dequeue”, which is done at the other end of the queue called “front”.

FrontRear

Algorithm QINSERT (ITEM)

1.If (rear = maxsize-1 )print (“queue overflow”) and return

2.Else rear = rear + 1

Queue [rear] = item

Algorithm QDELETE ()

1.If (front =rear)print “queue empty” and return

2. Else Front = front + 1 item = queue [front]; Return item

Queue Applications

Real life examplesWaiting in lineWaiting on hold for tech support

Applications related to Computer ScienceRound robin schedulingJob scheduling (FIFO Scheduling)Key board buffer

3 states of the queue

1.Queue is emptyFRONT=REAR

2.Queue is fullREAR=N

3.Queue contains element >=1FRONT<REARNO. OF ELEMENT=REAR-FRONT+1

Representation Of Queues

1.Using an array2.Using linked list

Circular Queue To solve this problem, queues implement

wrapping around. Such queues are called Circular Queues.

Both the front and the rear pointers wrap around to the beginning of the array.

It is also called as “Ring buffer”. Items can inserted and deleted from a

queue in O(1) time.

Queue Example

+Queue()+insert() : void+remove() : long+peekFront() : long+isEmpty() : bool+isFull() : bool+size() : int

-maxSize : int-queueArray [] : long-front : int-rear : int-nItems : int

Queue

QueueApp

Interface1

Queue sample code C:\Documents and Settings\box\My Docume

nts\CS\CSC\220\ReaderPrograms\ReaderFiles\Chap04\Queue\queue.java

Various Queues Normal queue (FIFO) Circular Queue (Normal Queue) Double-ended Queue (Deque) Priority Queue

Deque It is a double-ended queue. Items can be inserted and deleted from

either ends. More versatile data structure than stack or

queue. E.g. policy-based application (e.g. low

priority go to the end, high go to the front) In a case where you want to sort the

queue once in a while, What sorting algorithm will you use?

Priority Queues More specialized data structure. Similar to Queue, having front and rear. Items are removed from the front. Items are ordered by key value so that the

item with the lowest key (or highest) is always at the front.

Items are inserted in proper position to maintain the order.

Let’s discuss complexity

Priority Queue Example

+Queue()+insert() : void+remove() : long+peekMin() : long+isEmpty() : bool+isFull() : bool

-maxSize : int-queueArray [] : long-nItems : int

PrioityQ

PriorityQApp

Interface1

Priority Queues Used in multitasking operating system. They are generally represented using

“heap” data structure. Insertion runs in O(n) time, deletion in O(1)

time. C:\Documents and Settings\box\My Documents\CS\CSC\220\ReaderPrograms\ReaderFiles\Chap04\PriorityQ\priorityQ.java

Parsing Arithmetic Expressions

2 + 3 2 + 4 * 5 ((2 + 4) * 7) + 3* (9 – 5))

Infix vs postfix Why do we want to do this

transformation?

• 2 3 +• 2 4 5 * +• 2 4 + 7 * 3 9 5 - * +

Infix to postfix Read ch from input until empty

◦ If ch is arg , output = output + arg◦ If ch is “(“, push ‘(‘;◦ If ch is op and higher than top push ch◦ If ch is “)” or end of input,

output = output + pop() until empty or top is “(“◦ Read next input

C:\Documents and Settings\box\My Documents\CS\CSC\220\ReaderPrograms\ReaderFiles\Chap04\Postfix\postfix.java

Postfix eval 5 + 2 * 3 -> 5 2 3 * + Algorithm

◦ While input is not empty◦ If ch is number , push (ch)◦ Else

Pop (a) Pop(b) Eval (ch, a, b)

C:\Documents and Settings\box\My Documents\CS\CSC\220\ReaderPrograms\ReaderFiles\Chap04\Postfix\postfix.java

Quick XML Review XML – Wave of the future

Another Real world example <?xml version = "1.0"?> <!-- An author --> <author> <name gender = "male"> <first> Art </first> <last> Gittleman </last> </name> </author>

THANK YOU